In general, if one has an inclusion of von Neumann algebras \({\mathcal {N}}\subset {\mathcal {M}}\) , this is said to be
split if there is a type I factor \({\mathcal {R}}\)  such that \({\mathcal {N}}\subset {\mathcal {R}}\subset {\mathcal {M}}\) .
Furthermore, if \({\mathcal {N}}\subset {\mathcal {M}}\)  is an inclusion of factors and \(\Omega \)  is cyclic and
separating for \({\mathcal {M}}\) , then the nuclearity of the map \({\mathcal {N}}\ni x \longmapsto \Delta ^{\frac{1}{4}}x\Omega \) 
implies the split property, where \(\Delta \)  is the modular operator for \({\mathcal {M}}\)  with respect to \(\Omega \) 
[1]}.
